We discuss properties and values of maximum matchings and minimum median problems for nite point sets. In particular, we consider \minimum stars", which are deened by a center chosen from the given point set, such that the total geometric distance min kStk to all the points in the set is minimized. If the center point is not required to be an element of the set (i. e., the center may be a Stein...

In this note, we show that one of the arguments used by Moazzami for computing the tenacity of the third Harary graph is wrong and then improve the proof. © 2014 Published by Elsevier B.V.

We discuss worst-case bounds on the ratio of maximum matching and minimum median values for finite point sets. In particular, we consider “minimum stars,” which are defined by a center chosen from the given point set, such that the total geometric distance L S to all the points in the set is minimized. If the center point is not required to be an element of the set (i.e., the center may be a St...

Mitchell S Steiner and Jeffrey R Gingrich Department of Urology, University of Tennessee, Memphis, Tennessee 38163 _________________________________________________________________________________________________ Correspondence: Mitchell S. Steiner, MD, Department of Urology, University of Tennessee Medical Center, 956 Court Avenue, Memphis, Tennessee 38163. Telephone: 901-448-1492; Fax: 901-44...

The power of Steiner points was studied in a number of different settings in the context of metric embeddings. Perhaps most notably in the context of probabilistic tree embeddings Bartal and Fakcharoenphol et al. [8, 9, 21] used Steiner points to devise near-optimal constructions of such embeddings. However, Konjevod et al. [24] and Gupta [22] demonstrated that Steiner points do not help in thi...

Properties of the 11 084 874 829 Steiner triple systems of order 19 are examined. In particular, there is exactly one 5-sparse, but no 6-sparse, STS(19); there is exactly one uniform STS(19); there are exactly two STS(19) with no almost parallel classes; all STS(19) have chromatic number 3; all have chromatic index 10, except for 4 075 designs with chromatic index 11 and two with chromatic inde...